If you don't already have your own personal domain and aren't ready to buy one, then you can use one of our completely free sub-domains. A free sub-domain is formatted as yournamehere.weebly.com.
If you're publishing for the first time, you'll be prompted to set your site address then. If you want to change this later, just go to Settings > General and click Change next to the site address.
On the next screen, type in the text of the subdomain you want to use for your site in the search box. This process will check to make sure the subdomain isn't taken and will also check for any available domain names that match.
Click Choose next to the subdomain on this screen to set the site address. Make sure to publish again so your site will be live at the new address!